Well the psp 1000 have a really retarded joystick placed on the faceplate so if the faceplate isn't secured tightly in place it acts wierd . So first make sure the faceplate is placed well & tight all screws in one is a little loose . If that doesn't help then you will need a plugin called JoySens . First try tinkering with it a little to make the joystick work if your joystick is stuck in the same position( I am too tired now to type exact details so try figuring it out & if you failed I will write something). If your joystick however is floating free inside then you will need to replace it but you can use JoySens to completly disable it & play only with the butons till you get it replaced .

I guess you didn't bother reading the FAQ or readme included on how to use it so here is what you should do copied from the readme .

First make sure its enabled by pressing NOTE + SELECT

Second follow this steps to center the analog

- Move the analog stick to the top-left and hold it a few seconds, then release slowly until it's centered and don't
touch it anymore. Press NOTE+SQUARE,
- Move the analog stick to the bottom-right and hold a few seconds, release slowly until centered. Press NOTE+SQUARE.
- Repeat these steps until the center point has been found correctly (optimally, this is the mean value of the axes
minimal and maximal value when the stick isn't touched).

After that try a game & see it works . If not then you have to completely disable the analog completely by pressing NOTE + DOWN till the adjust value is zero or if the game require the analog check the readme on remapping choices .